We offer an explanation for the correlation between the minimum variability timescale (MT S) in the prompt emission light curve of gamma-ray bursts (GRBs) and the estimated bulk Lorentz factor of these GRBs, in the context of a magnetically arrested disk (MAD) model. In particular, we show that previously derived limits on the maximum available energy per baryon in a Blandford-Znajek jet leads to a relationship between the characteristic MAD timescale, t M AD , in GRBs and the maximum bulk Lorentz factor: t M AD ∝ Γ −6 , somewhat steeper than (although within the error bars of) the fitted relationship found in the GRB data. Similarly, the MAD model also naturally accounts for the observed anti-correlation between MT S and gamma-ray luminosity L in the GRB data, and we estimate the accretion rates of the GRB disk (given these luminosities) in the context of this model. Both of these correlations (MT S − Γ and MT S − L) are also observed in the AGN data, and we discuss the implications of our results in the context of both GRB and blazar systems.